Exercise 13 Page 622

Let's separate the two triangles and then add the given information. Note that △ ADC and △ ABD both share AD as a side so in addition to the given information, we can say by the Reflexive Property of Congruence that these sides are congruent.

Having separated the triangles and added the given information, we can by the HL Congruence Theorem claim that the two triangles are congruent. Let's write this as a two-column proof.

Statement	Reason
1. &AC≅ BD & AB⊥ AD & CD ⊥ AD	1. Given
2. AD ≅ AD	2. Reflexive Property of Congruence
3. ∠ BAD and ∠ CDA are right angles	3. Definition of perpendicular lines
4. ∠ BAD and ∠ CDA are right triangles	4. Definition of a right triangle
5. ∠ BAD ≅ ∠ CDA	5. HL congruence theorem.